Press and hold the Power button for 10-15 seconds. Then leave it for 20-30 seconds and see if it restarts.

To REBOOT:
Press and HOLD all three keys for about 10 - 20 seconds: PowerOn, VolUp and VolDown. Start with the PowerButton. Keep holding past the 3-choice options screen. If you hear a shutter type sound, you've taken a Screen Shot and probably missed the PowerButton.
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If that fails:

The PB has a one year warranty to the original purchaser. It also has 90 free Tech support. I do not know how Rim deals with "quasi-tech support v. warranty"

Rim Support
Tel:
canada Toll Free: 1-877-644-8405
United States Toll Free: 1-877-644-8410
Puerto Rico Toll Free: 1-855-651-4936
Email: playbooksupport@blackberry.com (this route generally does not work and a call is necessary)

Had a similar issue after taking my playbook on my bike one cold and foggy morning. The playbook just quit responding so I turned it off and let it set for a little while. When I turned it on again, the screen was not responsive in some areas. I took a hair dryer and warmed the screen and that seemed to help, so I plugged the charger in and played a movie for eight hours to warm the tablet from the inside and finally got the screen working better than ever. Got lucky I guess. Just a testament on how well built the PlayBook ™ really is. Good luck on your issue.

same thing happend to me... i thought it was done for. I turned it off fully charged, and left it for about a week. just turned it on randomly one day not expecting anything and surprisingly it worked. not sure why this worked, just know it did, surprised me